User:Matthew Vandermast/Prime signature index

First integer of each prime signature: A025487

Prime signature of n: A212171 (nonincreasing version), A118914 (nondecreasing version)

Sequences where prime signature of n determines a(n): for each sequence, page indicates largest integer k such that a(n) depends only on the multiset of the exponents >=k in n's prime factorization (k=1 if no number is given in parentheses):

Additive: A001221, A001222, A046660(2), A056169, A056170(2).

Multiplicative, number of factorizations of different types: A000005, A000688(2), A050361(3), A050377(2),

Multiplicative, other: A005361(2), A007425, A008683, A008836, A008966(2), A034444, A037445, A038538(2), A046951(2), A049419(2), A056624(2), A061704(3), A063775(4), A162510(2), A162511(2), A181819, A212181(2).

Number of factorizations of different types, non-multiplicative: A001055, A008480, A045778, A050320, A050326, A050328, A050330, A050332, A050334, A050336, A050338, A050340, A050345, A050347, A050349, A050354, A050356, A050358, A050363, A050370, A050372, A050374, A050379, A051707?, A074206, A077565,

Other: A007424(2), A008481 A010553, A038548, A051707?, A051903 (2 for n>1), A056626(3), A066301(2), A071325(2), A071625, A072411(2), A076078, A085082, A086435?, A088873, A091050(2), A107078(2), A114717, A119842, A181796, A185102 (2 for n>1), A212180(2).

Tables such that prime signature of n determines row n: A146289, A146291.

Permutations of A025487: A036035, A059901, A063008, A077569, A085988(extend), A086141, A087443, A108951, A131886, A136101?, A136103?, A181812, A181821, A181822, A212638.

Subsequences of A025487:

Sequences of record-setters for prime signature functions: A000079 (A001222); A000142(A086435); A002110(A001221); A002182(A000005); A006939(A071625); A097212(A076078); A126098(A018892); A182862(A182860)

Sequences of record-setters for other functions: A051451, A181806

r-s combo platters A070175 A168263 A168264 A181809

n such that a(n) is a new distinct value of a prime signature function A007416(A000005) A119840(A114717), A119845 A108951 A181821

Other: A001013, A056153 (comment here; odd A181815), A056836, A064783, A066120(r-s), A085929, A087980, A097213, A129912, A134865, A140999, A161812(edit,extend), A166470, A166472, A166473, A166475(r-s), A167448(r-s), A181555(r-s?), A181800, A181804, A181818(min), A212170(r-s)

All terms belong to A025487, other: LCM -> A003418, A056835,

Prime signature functions indexed by A025487: A036041(A001222); A050322(A001055); A050323(A045778); A050324(A074206-correct this!); A050325(A050320); A050327(-1); A050327(-1); A050329(-1); A050331(-1); A050333(-1); A050335(-1); A050337(-1); A050339(-1); A050341(-1); A050346(-1); A050348(-1); A050350(-1); A050355(-1); A050357(-1); A050359(-1); A050360(A000688); A050362(-1); A050364(-1); A050371(-1); A050373(-1); A050378(-1); A050380(-1); A050382(A008480); A051282(A051903); A052304(A046951); A052305(A038538); A052306(A005361); A087437(A077565); A097211(A076078); A108504(A038548); A108460(A051707); A146288(A000005); A174524(A066637); A181815(tbd); A181820(-1); A212178(A056170)

Other function indexed by A025487: A098887

Unclassified: A025488 A035206 A035341 A051466 A051707? (fact. of (n,n) into pairs (j,k) that satisfy j>1, k>=1) A052213 A052214 A056099

Also: (A25487 in title) A035310 A057567 A060826 A061394 A064839 A073039 A077560 A077561 A077562 A083435 A090323 A096903? A098120 A098718 A098719 A099992 A099993 A108462 A108463 A108464 A0108466 A108467 A124832 A146290,A146292 A178810 A178811 A181811 A181813 A181814 A181815 A181816 A181817 A181820 A181823-A181827 A182762 A182763 A182764 A182861 A182863 A212175

(A025487 not in title, but in sequence) A035796 A046523 A056823 A062515 A074140 A080688?? A085089 A085612 A085643? A085834* A085986 A085987 A092271? A093936?? A095904 A118314 A121457? A124058 A129305? A131420? A131801 A131802 A131888? A131997 A133928 A136102 A136624?? A138533?? A138534 A140691 A147516 A161360 A178799 A178849 A179216 A179983 A181807 A187448

(A025487 nowhere in sequence) A018892

prime signature: see also (1) A000688* A005361* A008480* A008683* A008966* A025488 A035206 A035341 A036035* A036041* A038538* A046660*

prime signature: see also (2) A046951* A050320* A050322* A050323* A050324* A050325* A050326* A050327* A050328 A050329 A050330 A050331 (all)

prime signature: see also (3) A050332 A050333 A050334 A050335 A050336 A050337 A050338 A050339 A050340 A050341 A050345 A050346 (all)

prime signature: see also (4) A050347 A050348 A050349 A050350 A050354 A050355 A050356 A050357 A050358 A050359 A050360 A050361 (all)

prime signature: see also (5) A050362 A050363 A050364 A050370 A050371 A050372 A050373 A050374 A050375 A050377 A050378 A050379 (all)

prime signature: see also (6) A050380* A050382* A051282* A051466 A051707 (fact. of (n,n) into pairs (j,k) that satisfy j>1, k>=1) A052213 (comment for A212652) A052214 A052304* A052305* A052306* A056099 A056153*

prime signature: see also (7) A056808 (does this belong?) A056823 (ditto; also don't understand) A057335 (ditto)

prime signature: see also (8) primes, in arithmetic progressions (??)

ops: A056808 A056823 A057335; A091405(edit); primally tight; also A096903 above; A055932; A096153

subsequence, false positive: A121853 (5932nd term is 1st exception)

also of interest: A191743